TY - JOUR
T1 - On inverse sum indeg energy of graphs
AU - Jamal, Fareeha
AU - Imran, Muhammad
AU - Rather, Bilal Ahmad
N1 - Publisher Copyright:
© 2023 the author(s).
PY - 2023/1/1
Y1 - 2023/1/1
N2 - For a simple graph with vertex set {v1, v2, ⋯, vn} and degree sequence dvi i = 1, 2, ⋯, n the inverse sum indeg matrix (ISI matrix) AISI(G) = (aij) of G is a square matrix of order n, where aij = dvidvj/dvi + dvj, if vi is adjacent to vj and 0, otherwise. The multiset of eigenvalues τ1 ≥ τ2 ≥ ⋯ ≥ τn of AISI(G) is known as the ISI spectrum of G. The ISI energy of G is the Σni=1 |τ| of the absolute ISI eigenvalues of G. In this article, we give some properties of the ISI eigenvalues of graphs. Also, we obtain the bounds of the ISI eigenvalues and characterize the extremal graphs. Furthermore, we construct pairs of ISI equienergetic graphs for each n≥ 9.
AB - For a simple graph with vertex set {v1, v2, ⋯, vn} and degree sequence dvi i = 1, 2, ⋯, n the inverse sum indeg matrix (ISI matrix) AISI(G) = (aij) of G is a square matrix of order n, where aij = dvidvj/dvi + dvj, if vi is adjacent to vj and 0, otherwise. The multiset of eigenvalues τ1 ≥ τ2 ≥ ⋯ ≥ τn of AISI(G) is known as the ISI spectrum of G. The ISI energy of G is the Σni=1 |τ| of the absolute ISI eigenvalues of G. In this article, we give some properties of the ISI eigenvalues of graphs. Also, we obtain the bounds of the ISI eigenvalues and characterize the extremal graphs. Furthermore, we construct pairs of ISI equienergetic graphs for each n≥ 9.
KW - adjacency matrix
KW - energy
KW - inverse sum indeg matrix
KW - topological indices
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U2 - 10.1515/spma-2022-0175
DO - 10.1515/spma-2022-0175
M3 - Article
AN - SCOPUS:85144735047
SN - 2300-7451
VL - 11
JO - Special Matrices
JF - Special Matrices
IS - 1
ER -